Surface Green`s functions and boundary modes using impurities: Weyl semimetals and topological insulators

In this work we provide a direct and non-numerical technique to obtain the surface Green's functions for three-dimensional systems. This technique is based on the ideas presented by V. Kaladzhyan and C. Bena [Phys. Rev. B 100, 081106(R) (2019)], in which we start with an infinite system and model the boundary using a planelike infinite-amplitude potential. Such a configuration can be solved exactly using the T-matrix formalism. We apply our method to calculate the surface Green's function and the corresponding Fermi-arc states for Weyl semimetals. We also apply the technique to systems of lower dimensions, such as Kane-Mele and Chern insulator models, to provide a more efficient and non-numerical method to describe the formation of edge states.